{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FOPBDRAAHQXRLICXOZJCFNP5PT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fc578726cce5590409fbc3d939cba12a258a1c323448e8052921ac03f27aa78c","cross_cats_sorted":["math.AG","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2020-12-22T12:31:28Z","title_canon_sha256":"1b83f517fc914aa33521b0d6f0fa545ee3d12dc9b9de79232e7a11728f7b6988"},"schema_version":"1.0","source":{"id":"2012.11961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11961","created_at":"2026-07-05T02:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11961v1","created_at":"2026-07-05T02:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11961","created_at":"2026-07-05T02:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"FOPBDRAAHQXR","created_at":"2026-07-05T02:01:23Z"},{"alias_kind":"pith_short_16","alias_value":"FOPBDRAAHQXRLICX","created_at":"2026-07-05T02:01:23Z"},{"alias_kind":"pith_short_8","alias_value":"FOPBDRAA","created_at":"2026-07-05T02:01:23Z"}],"graph_snapshots":[{"event_id":"sha256:533233220c967221af799d0b8e6a931b9aea6d29553ae5dfc4c97d1886253e85","target":"graph","created_at":"2026-07-05T02:01:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.11961/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we will generalize some results in Manin's paper \"Three-dimensional hyperbolic geometry as $\\infty$-adic Arakelov geometry\" to the supergeometric setting. More precisely, viewing $\\mathbb{C}^{1|1}$ as the boundary of the hyperbolic superspace $\\mathcal{H}^{3|2}$, we reexpress the super-Green functions on the supersphere $\\hat{\\mathbb{C}}^{1|1}$ and the supertorus $T^{1|1}$ by some data derived from the supergeodesics in $\\mathcal{H}^{3|2}$.","authors_text":"Runhong Zong, Zhi Hu","cross_cats":["math.AG","math.MP"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2020-12-22T12:31:28Z","title":"Hyperbolic Superspaces and Super-Riemann Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11961","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:57956c36d5046bb02a0702a5ea2a56a58f6dcbc4991b0eb8ed18c2585be91353","target":"record","created_at":"2026-07-05T02:01:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fc578726cce5590409fbc3d939cba12a258a1c323448e8052921ac03f27aa78c","cross_cats_sorted":["math.AG","math.MP"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math-ph","submitted_at":"2020-12-22T12:31:28Z","title_canon_sha256":"1b83f517fc914aa33521b0d6f0fa545ee3d12dc9b9de79232e7a11728f7b6988"},"schema_version":"1.0","source":{"id":"2012.11961","kind":"arxiv","version":1}},"canonical_sha256":"2b9e11c4003c2f15a057765222b5fd7ccb594e5ca83224f56d4d016a46a48db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b9e11c4003c2f15a057765222b5fd7ccb594e5ca83224f56d4d016a46a48db3","first_computed_at":"2026-07-05T02:01:23.340632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:01:23.340632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rwgCp28UTH1jQXxx6s1xSWYcAFErZM0dPEBBu6R2suB1/ZEjaBgorvwRxffJviY4yzsh4n1Styzd7Mvc4sMtAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:01:23.341021Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.11961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57956c36d5046bb02a0702a5ea2a56a58f6dcbc4991b0eb8ed18c2585be91353","sha256:533233220c967221af799d0b8e6a931b9aea6d29553ae5dfc4c97d1886253e85"],"state_sha256":"d44582dcbf1b63506dad822bdfdb294f903740e1530c1910dc0f1e97859fdc6d"}